Numerical Solution of Riemann–Hilbert Problems: Painlevé II

We describe a new, spectrally accurate method for solving matrix-valued Riemann–Hilbert problems numerically. The effectiveness of this approach is demonstrated by computing solutions to the homogeneous Painlevé II equation. This can be used to relate initial conditions with asymptotic behavior.

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Bibliographic Details
Published inFoundations of computational mathematics Vol. 11; no. 2; pp. 153 - 179
Main Author Olver, Sheehan
Format Journal Article
LanguageEnglish
Published New York Springer-Verlag 01.04.2011
Springer
Springer Nature B.V
Subjects
Applications of Mathematics
Computer Science
Differential equations
Economics
Linear and Multilinear Algebras
Math Applications in Computer Science
Mathematics
Mathematics and Statistics
Matrix
Matrix Theory
Numerical Analysis
Problem solving
Iran
Painlevé transcendents
Collocation methods
65E05
33E17
Spectral methods
30E25
Riemann–Hilbert problems
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ISSN1615-3375
1615-3383
DOI10.1007/s10208-010-9079-8

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Summary:We describe a new, spectrally accurate method for solving matrix-valued Riemann–Hilbert problems numerically. The effectiveness of this approach is demonstrated by computing solutions to the homogeneous Painlevé II equation. This can be used to relate initial conditions with asymptotic behavior.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-010-9079-8